Clustering and classification problems arise in a wide range of application settings from clustering documents, placing centers in networks, to image processing, biometric analysis, language modeling and the categorization of hypertext documents. The applications mentioned above give rise to a number of related algorithms problems, each of which are NP-complete.  Some of the general techniques, and recent developments in approximation algorithms for these problems are surveyed. From the Series:CSE Colloquia - 1999